Where we are, schools can administer achievement tests without consent. I believe that they do seek consent for IQ or group ability tests and if they intend to test on a non-standard measure of achievement. For instance, everyone might be given the MAPs tests, NCLB state tests, DRA reading, SRI lexile, etc. at some point. However, they rarely, if ever, give tests like individual achievement tests such as the WJ-III or WIAT. If they are going to test on something like that, parents are usually informed ahead of time and, I imagine, permission could be denied.
I suspect that is b/c the former achievement measures are seen as standard measures of growth and achievement that are used for placement and the latter are used only when specific concerns exist or at parent request.